Searches , social queries for COXETER GROUP
Search references for COXETER GROUP. Phrases containing COXETER GROUP
See searches and references containing COXETER GROUP!
Search references for COXETER GROUP. Phrases containing COXETER GROUP
See searches and references containing COXETER GROUP!COXETER GROUP
Group that admits a formal description in terms of reflections
In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic
Coxeter_group
Group of geometric symmetries with at least one fixed point
n Coxeter group has n mirrors and is represented by a Coxeter–Dynkin diagram. Coxeter notation offers a bracketed notation equivalent to the Coxeter diagram
Point_group
Pictorial representation of symmetry
Coxeter–Dynkin diagram (or Coxeter diagram, Coxeter graph) is a graph with numerically labeled edges (called branches) representing a Coxeter group or
Coxeter–Dynkin_diagram
Canadian geometer (1907–2003)
geometry and group theory are named after him, including the Coxeter graph, Coxeter groups, Coxeter's loxodromic sequence of tangent circles, Coxeter–Dynkin
H._S._M._Coxeter
Subgroup of a root system's isometry group
reflection group. In fact it turns out that most finite reflection groups are Weyl groups. Abstractly, Weyl groups are finite Coxeter groups, and are important
Weyl_group
Deformation of the group algebra of a Coxeter group
deformation of the group algebra of a Coxeter group. The Hecke algebra can also be viewed as a q-analog of the group algebra of a Coxeter group. Hecke algebras
Iwahori–Hecke_algebra
Concept in geometry
In mathematics, a Coxeter element is an element of an irreducible Coxeter group which is a product of all simple reflections. The product depends on the
Coxeter_element
Unsolved problem in mathematics Given two Coxeter groups Γ 1 {\displaystyle \Gamma _{1}} and Γ 2 {\displaystyle \Gamma _{2}} , decide whether W ( Γ 1 )
Isomorphism problem of Coxeter groups
Isomorphism_problem_of_Coxeter_groups
Classification system for symmetry groups in geometry
Coxeter notation (also Coxeter symbol) is a system of classifying symmetry groups, describing the angles between fundamental reflections of a Coxeter
Coxeter_notation
Groups of point isometries in 3 dimensions
passing through the same point are the finite Coxeter groups, represented by Coxeter notation. The point groups in three dimensions are widely used in chemistry
Point groups in three dimensions
Point_groups_in_three_dimensions
Pictorial representation of symmetry
special kind of Coxeter diagram), the Weyl group (a concrete reflection group), or the abstract Coxeter group. Although the Weyl group is abstractly isomorphic
Dynkin_diagram
Simplicial complex
mathematics, the Coxeter complex, named after H. S. M. Coxeter, is a geometrical structure (a simplicial complex) associated to a Coxeter group. Coxeter complexes
Coxeter_complex
3D symmetry group
of 120. The full symmetry group is the Coxeter group of type H3. It may be represented by Coxeter notation [5,3] and Coxeter diagram . The set of rotational
Icosahedral_symmetry
Concept in mathematics
symmetric group of permutations, the dihedral groups, and more generally all finite real reflection groups (the Coxeter groups or Weyl groups, including
Complex_reflection_group
Family of infinite discrete groups
with Coxeter groups. Examples are free groups, free abelian groups, braid groups, and right-angled Artin–Tits groups, among others. The groups are named
Artin–Tits_group
Symmetric subdivision in hyperbolic geometry
(7 3 2) triangle group, Coxeter group [7,3], orbifold (*732) contains these uniform tilings: The (8 3 2) triangle group, Coxeter group [8,3], orbifold
Uniform tilings in hyperbolic plane
Uniform_tilings_in_hyperbolic_plane
Mathematical group
The symmetric group belongs to a larger family of reflection groups called Coxeter groups, each of which comes with a special generating set S (generalizing
Parabolic subgroup of a reflection group
Parabolic_subgroup_of_a_reflection_group
Integral polynomial
indexed by pairs of elements y, w of a Coxeter group W, which can in particular be the Weyl group of a Lie group. In the spring of 1978 Kazhdan and Lusztig
Kazhdan–Lusztig_polynomial
Group of symmetries of an n-dimensional hypercube
The family of hyperoctahedral groups forms type B in the classification of finite Coxeter groups. The hyperoctahedral groups were named by Alfred Young in
Hyperoctahedral_group
Connected non-abelian Lie group lacking nontrivial connected normal subgroups
series groups are all simply laced, but no group of type B, C, F, or G is simply laced. Cartan matrix Coxeter matrix Weyl group Coxeter group Kac–Moody
Simple_Lie_group
Spatial tiling of convex uniform polyhedra
other forms based on the ring patterns of the Coxeter diagram. The fundamental infinite Coxeter groups for 3-space are: The C ~ 3 {\displaystyle {\tilde
Convex_uniform_honeycomb
Discrete group type in group theory
reflection group. Reflection groups also include Weyl groups and crystallographic Coxeter groups. While the orthogonal group is generated by reflections
Reflection_group
Type of group in mathematics
groups in two dimensions. Other finite subgroups include: Permutation matrices (the Coxeter group An) Signed permutation matrices (the Coxeter group Bn);
Orthogonal_group
Uniform 6-dimensional polytope
from a small set of symmetry groups. These construction operations are represented by the permutations of rings of the Coxeter-Dynkin diagrams. Each combination
Uniform_6-polytope
Tessellation of convex uniform polyhedron cells
23 Coxeter group families of paracompact uniform honeycombs, generated as Wythoff constructions, and represented by ring permutations of the Coxeter diagrams
Paracompact uniform honeycombs
Paracompact_uniform_honeycombs
Type of group in abstract algebra
theory of Coxeter groups, the symmetric group is the Coxeter group of type An and occurs as the Weyl group of the general linear group. In combinatorics
Symmetric_group
Unique element of maximal length in a finite Coxeter group
mathematics, the longest element of a Coxeter group is the unique element of maximal length in a finite Coxeter group with respect to the chosen generating
Longest element of a Coxeter group
Longest_element_of_a_Coxeter_group
Uniform 6-polytope
from the E6 group. It was first published in E. L. Elte's 1912 listing of semiregular polytopes, named as V72 (for its 72 vertices). Its Coxeter symbol is
1_22_polytope
be visualized as symmetric orthographic projections in Coxeter planes of the E8 Coxeter group, and other subgroups. Symmetric orthographic projections
E8_polytope
Group of irregular uniform polytopes
In geometry, the Gosset–Elte figures, named by Coxeter after Thorold Gosset and E. L. Elte, are a group of uniform polytopes which are not regular, generated
Gosset–Elte_figures
Regular tiling of hyperbolic 3-space
the [5,3,4] Coxeter group family, including this regular form. There are eleven uniform honeycombs in the bifurcating [5,31,1] Coxeter group family, including
Order-4 dodecahedral honeycomb
Order-4_dodecahedral_honeycomb
Number line and triangular tiling's symmetry mathematical structure
Coxeter groups, so the affine symmetric groups are Coxeter groups, with the s i {\displaystyle s_{i}} as their Coxeter generating sets. Each Coxeter group
Affine_symmetric_group
Infinite regular skew polyhedron
Harold Scott MacDonald Coxeter derived a third, the mutetrahedron, and proved that these three were complete. Under Coxeter and Petrie's definition,
Regular_skew_apeirohedron
Polytope with highest degree of symmetry
by their isometry group. These are finite Coxeter groups, but not every finite Coxeter group may be realised as the isometry group of a regular polytope
Regular_polytope
5-dimensional hypercube
x1, x2, x3, x4) with −1 < xi < 1 for all i. n-cube Coxeter plane projections in the Bk Coxeter groups project into k-cube graphs, with power of two vertices
5-cube
Tiling of hyperbolic 3-space by uniform polyhedra
polyhedral cells. In 3-dimensional hyperbolic space there are nine Coxeter group families of compact convex uniform honeycombs, generated as Wythoff
Uniform honeycombs in hyperbolic space
Uniform_honeycombs_in_hyperbolic_space
Space-filling tessellation
{A}}_{3}} Coxeter group. This honeycomb has four uniform constructions, with the truncated octahedral cells having different Coxeter groups and Wythoff
Bitruncated_cubic_honeycomb
symmetrically-ringed Coxeter-Dynkin diagram. The runcinated 6-simplexes are in a set of 35 uniform 6-polytopes based on the [3,3,3,3,3] Coxeter group, all shown
Runcinated_6-simplexes
Schläfli symbol {3,71,1}, Coxeter diagram, , with alternating types or colors of order-7 triangular tiling cells. In Coxeter notation the half symmetry
Order-7-3 triangular honeycomb
Order-7-3_triangular_honeycomb
tilings around every edge. In Coxeter notation, the removal of the 3rd and 4th mirrors, [3,6,3*] creates a new Coxeter group [3[3,3]], , subgroup index 6
Triangular_tiling_honeycomb
Type of geometrical object
symmetry can be generated by these three Coxeter groups, represented by permutations of rings of the Coxeter-Dynkin diagrams: Selected regular and uniform
Uniform_10-polytope
Uniform 7-dimensional polytope
symmetry of the E7 group. It was discovered by Thorold Gosset, published in his 1900 paper. He called it a 7-ic semi-regular figure. Its Coxeter symbol is 321
3_21_polytope
Uniform polytope
uniform polytope, constructed from the E7 group. Its Coxeter symbol is 132, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the
1_32_polytope
Symmetry group in 1D systems
the affine Coxeter group [∞], or Coxeter-Dynkin diagram representing two reflections, and the translational symmetry as [∞]+, or Coxeter-Dynkin diagram
One-dimensional symmetry group
One-dimensional_symmetry_group
set of 35 uniform 6-polytopes based on the [3,3,3,3,3] Coxeter group, all shown here in A6 Coxeter plane orthographic projections. Klitzing, (x3o3o3o3x3o
Stericated_6-simplexes
part of 19 uniform 5-polytopes based on the [3,3,3,3] Coxeter group, all shown here in A5 Coxeter plane orthographic projections. (Vertices are colored
Stericated_5-simplexes
Polytope in 8-dimensional geometry
symmetry of the E8 group. It was discovered by Thorold Gosset, published in his 1900 paper. He called it an 8-ic semi-regular figure. Its Coxeter symbol is 421
4_21_polytope
Bowers) There are two Coxeter groups associated with the cantellated 6-orthoplex, one with the B6 or [4,3,3,3,3] Coxeter group, and a lower symmetry with
Cantellated_6-orthoplexes
hyperbolic group, so either facets or vertex figures will not be bounded. E10 is last of the series of Coxeter groups with a bifurcated Coxeter-Dynkin diagram
E9_honeycomb
Seven-dimensional geometric object
for Coxeter plane graphs of these polytopes. The E7 Coxeter group has order 2,903,040. There are 127 forms based on all permutations of the Coxeter-Dynkin
Uniform_7-polytope
Mathematical group
Bi=M\wr \mathbb {Z} _{2}.\,} The Bimonster is also a quotient of the Coxeter group corresponding to the Dynkin diagram Y555, a Y-shaped graph with 16 nodes:
Bimonster_group
Regular paracompact honeycomb
paracompact. It is one of 15 uniform paracompact honeycombs in the [6,3,3] Coxeter group, along with its dual, the order-6 tetrahedral honeycomb. It is part
Hexagonal_tiling_honeycomb
6-dimensional hypercube
Coxeter groups associated with the 6-cube, one regular, with the C6 or [4,3,3,3,3] Coxeter group, and a half symmetry (D6) or [33,1,1] Coxeter group.
6-cube
Convex regular 5-polytope in geometry
There are three Coxeter groups associated with the 5-orthoplex, one regular, dual of the penteract with the C5 or [4,3,3,3] Coxeter group, and a lower symmetry
5-orthoplex
Quasiregular space-filling tesselation
{\displaystyle {\tilde {A}}_{3}} Coxeter group. The symmetry can be multiplied by the symmetry of rings in the Coxeter–Dynkin diagrams: The cantic cubic
Tetrahedral-octahedral honeycomb
Tetrahedral-octahedral_honeycomb
Natural number
generated from the abstract hypercubic B 6 {\displaystyle \mathrm {B_{6}} } Coxeter group (sometimes, the demicube is also included in this family), that is associated
63_(number)
Uniform 6-polytope
It is also called the Schläfli polytope. Its Coxeter symbol is 221, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the end
2_21_polytope
Regular tiling of hyperbolic 3-space
composed of pentagons: There are nine uniform honeycombs in the [3,5,3] Coxeter group family, including this regular form as well as the bitruncated form
Icosahedral_honeycomb
Group-theoretic generalization of matroids
In mathematics, Coxeter matroids are generalization of matroids depending on a choice of a Coxeter group W and a parabolic subgroup P. Ordinary matroids
Coxeter_matroid
Nonabelian group of order 120
octahedral group, 2O=⟨2,3,4⟩, order 48 Coxeter & Moser: Generators and Relations for Discrete Groups: <l,m,n>: Rl = Sm = Tn = RST Coxeter, H.S.M. (1940)
Binary_icosahedral_group
be visualized as symmetric orthographic projections in Coxeter planes of the E6 Coxeter group, and other subgroups. Symmetric orthographic projections
E6_polytope
Simple Lie group; the automorphism group of the octonions
and B is isomorphic to A₂. Its Weyl/Coxeter group G = W ( G 2 ) {\displaystyle G=W(G_{2})} is the dihedral group D 6 {\displaystyle D_{6}} of order 12
G2_(mathematics)
A 4-node Coxeter-Dynkin diagram represents this tetrahedral graph with order-2 edges hidden. If many edges are order 2, the Coxeter group can be represented
Goursat_tetrahedron
52-dimensional exceptional simple Lie group
Dynkin diagram for F4 is: . Its Weyl/Coxeter group G = W(F4) is the symmetry group of the 24-cell: it is a solvable group of order 1152. It has minimal faithful
F4_(mathematics)
Four-dimensional analogue of the tetrahedron
pentachoron, pentatope, pentahedroid, tetrahedral pyramid, or 4-simplex (Coxeter's α4 polytope), the simplest possible convex 4-polytope, and is analogous
5-cell
Uniform Polytope
uniform polytope, constructed from the E7 group. Its Coxeter symbol is 231, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the
2_31_polytope
Classification of a two-dimensional repetitive pattern
Coxeter notation (rectangular): [∞,2,∞] or [∞]×[∞] Coxeter notation (square): [4,1+,4] or [1+,4,4,1+] Lattice: rectangular Point group: D2 The group pmm
Wallpaper_group
Natural number
the group K5. There are five fundamental mirror symmetry point group families in 4-dimensions. There are also 5 compact hyperbolic Coxeter groups, or
5
Regular polytope whose 2D form is a pentagon
polytope in n dimensions constructed from the Hn Coxeter group. The family was named by H. S. M. Coxeter, because the two-dimensional pentagonal polytope
Pentagonal_polytope
Uniform polytope in 8 dimensional geometry
constructed within the symmetry of the E8 group. Its Coxeter symbol is 241, describing its bifurcating Coxeter-Dynkin diagram, with a single ring on the
2_41_polytope
gobpoxog). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by
Runcinated_6-cubes
Four-dimensional analogue of the cube
measure polytope, taken as a unit for hypervolume. Harold Scott MacDonald Coxeter labels it the γ4 polytope. The term hypercube without a dimension reference
Tesseract
Type of 7-polytope
guph). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by
Hexicated_7-simplexes
Regular tiling of hyperbolic 3-space
hyperbolic space: There are fifteen uniform honeycombs in the [5,3,4] Coxeter group family, including the order-5 cubic honeycomb as the regular form: The
Order-5_cubic_honeycomb
gibpo) H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by
Runcinated_7-simplexes
gacnet). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by
Stericated_5-cubes
Mathematical structure
defining a building Δ is a Coxeter group W, which determines a highly symmetrical simplicial complex Σ = Σ(W, S), called the Coxeter complex. A building Δ
Building_(mathematics)
degrees. Coxeter decompositions are named after Harold Scott MacDonald Coxeter, an accomplished 20th century geometer. He introduced the Coxeter group, an
Coxeter decompositions of hyperbolic polygons
Coxeter_decompositions_of_hyperbolic_polygons
Notation for polytopes and tessellations
instead [p,q,r,...]. Such groups are often named by the regular polytopes they generate. For example, [3,3] is the Coxeter group for reflective tetrahedral
Schläfli_symbol
set of 19 uniform 5-polytopes based on the [3,3,3,3] Coxeter group, all shown here in A5 Coxeter plane orthographic projections. (Vertices are colored
Runcinated_5-simplexes
four-dimensional crystal classes 1985 H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, Coxeter notation for 4D point groups 2003 John Conway and Smith, On Quaternions
Point groups in four dimensions
Point_groups_in_four_dimensions
American mathematician (born 1949)
is the author of two books that include The Geometry and Topology of Coxeter Groups and Multiaxial Actions on Manifolds. His notable contributions to the
Michael_W._Davis
Uniform 6-polytope
set of 35 uniform 6-polytopes based on the [3,3,3,3,3] Coxeter group, all shown here in A6 Coxeter plane orthographic projections. Klitzing, (x3o3o3o3o3x
Pentellated_6-simplexes
Schläfli symbol {3,81,1}, Coxeter diagram, , with alternating types or colors of order-8 triangular tiling cells. In Coxeter notation the half symmetry
Order-8-3 triangular honeycomb
Order-8-3_triangular_honeycomb
Skew polygon derived from a polytope
question is the Coxeter plane of the symmetry group of the polygon, and the number of sides, h, is the Coxeter number of the Coxeter group. These polygons
Petrie_polygon
be). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by
Truncated_8-simplexes
Partial order on a Coxeter group
or Chevalley–Bruhat order) is a partial order on the elements of a Coxeter group, that corresponds to the inclusion order on Schubert varieties. The
Bruhat_order
gabach). H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by
Stericated_7-simplexes
generated Coxeter groups Geometrically finite groups Baumslag–Solitar groups Non-Euclidean nilpotent groups Not every CAT(0) group is biautomatic A group is
Automatic_group
also one of 19 uniform polytera based on the [3,3,3,3] Coxeter group, all shown here in A5 Coxeter plane orthographic projections. (Vertices are colored
Rectified_5-simplexes
mathematics, the nil-Coxeter algebra, introduced by Fomin & Stanley (1994), is an algebra similar to the group algebra of a Coxeter group except that the generators
Nil-Coxeter_algebra
Vertex-transitive tiling of the plane by regular polygons
more details.) Coxeter groups for the plane define the Wythoff construction and can be represented by Coxeter-Dynkin diagrams: For groups with integer reflection
Uniform_tiling
Geometric object
from the En Coxeter group, and having only regular polytope facets. The family was named by their Coxeter symbol k21 by its bifurcating Coxeter–Dynkin diagram
Uniform_k_21_polytope
honeycomb, Schläfli symbol {3,(3,4,3)}, Coxeter diagram, , with alternating types or colors of tetrahedral cells. In Coxeter notation the half symmetry is [3
Order-7_tetrahedral_honeycomb
set of 19 uniform 5-polytopes based on the [3,3,3,3] Coxeter group, all shown here in A5 Coxeter plane orthographic projections. (Vertices are colored
Cantellated_5-simplexes
Isogonal polyhedron with regular faces
symbol (3 3 2). It can also be represented by the Coxeter group A2 or [3,3], as well as a Coxeter diagram: . There are 24 triangles, visible in the faces
Uniform_polyhedron
Topics referred to by the same term
type Coxeter group of finite type, a Coxeter group whose Schläfli matrix has only positive eigenvalues Coxeter matrix of finite type, a Coxeter matrix
Finite_type
Distance-regular graph with 56 vertices
isomorphic to the Schläfli graph. The automorphism group of the Gosset graph is isomorphic to the Coxeter group E7 and hence has order 2903040. The Gosset 321
Gosset_graph
gatrene) H.S.M. Coxeter: H.S.M. Coxeter, Regular Polytopes, 3rd edition, Dover, New York, 1973 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by
Cantellated_8-simplexes
In group theory, Matsumoto's theorem, proved by Hideya Matsumoto (1964), gives conditions for two reduced words of a Coxeter group to represent the same
Matsumoto's theorem (group theory)
Matsumoto's_theorem_(group_theory)
travel, tourism, insurance
COXETER GROUP
COXETER GROUP
Boy/Male
Indian
Desirable, Coveted, Pleasant
Boy/Male
Arabic, Hindu, Indian
Poeter
Boy/Male
Muslim/Islamic
Desirable coveted, agreeable
Girl/Female
Arabic, Muslim
Coveted; Desired
Surname or Lastname
English (Sussex)
English (Sussex) : unexplained.
Boy/Male
American, Australian, British, English, Irish
Young Horse; Frisky; Part of a Plough
Boy/Male
Indian
Desirable, Coveted, Pleasant
Boy/Male
Muslim
Desirable, Coveted, Pleasant
Surname or Lastname
Irish (co. Cork)
Irish (co. Cork) : reduced Anglicized form of Gaelic Mac Oitir ‘son of Oitir’, a personal name borrowed from Old Norse Óttarr, composed of the elements ótti ‘fear’, ‘dread’ + herr ‘army’.English : status name from Middle English cotter, a technical term in the feudal system for a serf or bond tenant who held a cottage by service rather than rent, from Old English cot ‘cottage’, ‘hut’ (see Coates) + -er agent suffix.Probably an Americanized spelling of German Kotter.
Girl/Female
Muslim
Coveted, Desired
Boy/Male
Arabic, Muslim
Agreeable; Desirable; Coveted
Boy/Male
English American
Horse herdsman. young horse;frisky.
Surname or Lastname
English
English : occupational name for someone who looked after asses and horses, from an agent derivative of Colt. Compare Coulthard.Variant spelling of German Kolter.
Surname or Lastname
English
English : metonymic occupational name for a grower or seller of costards (Anglo-Norman French, from coste ‘rib’), a variety of large apples, so called for their prominent ribs. In some cases, it may have been a nickname (from the same word) for a person with an apple-shaped (i.e. round) head.Dutch : status name for a churchwarden, from Late Latin custor ‘guard’, ‘warden’.Variant spelling of German Koster.This name is recorded in Beverwijck in New Netherland (Albany, NY) in the mid 17th century.
Surname or Lastname
English (Devon)
English (Devon) : occupational name for a treasurer or accountant, from Middle English counter (from Old French conteor).
Boy/Male
American, British, English
Colt Herder; Keeper of the Colt Herd; Horse Herdsman; Variant of Colt; Young Horse; Frisky
Boy/Male
English
young horse;frisky.
Boy/Male
Shakespearean
King Henry V' and 'Henry VI, Part 1' and 'King Henry the Sixth, Part III' Duke of Exeter, uncle...
Boy/Male
Muslim
Desirable, Coveted, Pleasant
Surname or Lastname
English
English : variant of Coster.
COXETER GROUP
COXETER GROUP
COXETER GROUP
COXETER GROUP
COXETER GROUP
COXETER GROUP
COXETER GROUP
travel, tourism, insurance